Analytical shape determination of fiber-like objects with Virtual Image Correlation

This paper reports a method allowing for the determination of the shape of deformed fiber-like objects. Compared to existing methods, it provides analytical results including the local slope and curvature which are of first importance, for instance, in beam mechanics. The presented VIC (Virtual Image Correlation) method consists in looking for the best correlation between the image of the fiber-like object and a virtual beam image, using an algorithm close to the Digital Image Correlation method developed in experimental solid mechanics. The computation only involves the part of the image in the vicinity of the fiber: the method is thus insensitive to the picture background and the computational cost remains low. Two examples are reported: the first proves the precision of the method, the second its ability to identify a complex shape with multiple loops.

💡 Research Summary

The paper introduces a novel image‑based technique called Virtual Image Correlation (VIC) for accurately determining the shape of deformed, fiber‑like objects. Traditional methods such as skeletonisation, edge tracking, or conventional Digital Image Correlation (DIC) can locate a fiber’s centreline but usually require separate post‑processing to obtain local slopes and curvatures, and they are highly sensitive to background noise and to complex geometries (loops, crossings). VIC overcomes these drawbacks by embedding a physically‑motivated virtual beam model directly into the correlation process.

The virtual beam is defined by a continuous curve parameterised by a set of coefficients θ (e.g., Bézier control points, Fourier series, or polynomial bases) together with a prescribed cross‑sectional intensity profile. By projecting this beam onto the image plane, a synthetic image V(x,y;θ) is generated. The method then minimises a correlation functional

C(θ)=∬_Ω